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An external pressure P is applied on a cube at `0^(@)C` so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and `alpha` is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by
A. `(3alpha)/(PK)`
B. `3 PK alpha`
C. `(P)/(3alpha K)`
D. `(P)/(alpha K)`

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Correct Answer - C
Bulk modulus of material, `K= (Delta p)/((-Delta V//V_(0)))` or `(Delta V)/(V_(0)) =(Delta p)/(K)` (in magnitude)
Due to thermal expansion for rise in temperature `Delta t`,
`V=V_(0)(1+gamma Delta t)=V_(0) + V_(0)gamma Delta t`
or `(V-V_(0))/(V_(0)) =gamma Delta t=3 alpha Delta t` `[.: gamma =3 alpha]`
or `(Delta V)/(V_(0)) =3alpha Delta t`
`:. (Delta p)/(K) =3alpha Delta t`
or `Delta t =(Delta p)/(3 alpha K) =(P)/(3 alpha K)` `[.: Delta p =p` (Given)]

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